A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit
Masaaki Fujii and
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Masaaki Fujii: Quantitative Finance Course, Graduate School of Economics, The University of Tokyo
Akihiko Takahashi: Quantitative Finance Course, Graduate School of Economics, The University of Tokyo
No CARF-F-495, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo
We investigate the problem of equilibrium price formation in an incomplete securities market. Each financial firm (agent) tries to minimize its cost via continuous-time trading with a securities exchange while facing the systemic and idiosyncratic noises as well as the stochastic order-flows from its over-the-counter clients. We have shown, in the accompanying paper (Fujii & Takahashi) , that the solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit. In this work, we prove the existence of a unique market clearing equilibrium among the heterogeneous agents of finite population size. We show the strong convergence to the corresponding mean-field limit given in  under suitable conditions. In particular, we provide the stability relation between the market clearing price for the heterogeneous agents and that for the homogeneous mean-field limit.
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